CPGD: Cadzow Plug-and-Play Gradient Descent for Generalised FRI

Finite rate of innovation (FRI) is a powerful reconstruction framework enabling the recovery of sparse Dirac streams from uniform low-pass filtered samples. An extension of this framework, called generalised FRI (genFRI), has been recently proposed for handling cases with arbitrary linear measurement models. In this context, signal reconstruction amounts to solving a joint constrained optimisation problem, yielding estimates of both the Fourier series coefficients of the Dirac stream and its so-called annihilating filter, involved in the regularisation term. This optimisation problem is however highly non convex and non linear in the data. Moreover, the proposed numerical solver is computationally intensive and without convergence guarantee. In this work, we propose an implicit formulation of the genFRI problem. To this end, we leverage a novel regularisation term which does not depend explicitly on the unknown annihilating filter yet enforces sufficient structure in the solution for stable recovery. The resulting optimisation problem is still non convex, but simpler since linear in the data and with less unknowns. We solve it by means of a provably convergent proximal gradient descent (PGD) method. Since the proximal step does not admit a simple closed-form expression, we propose an inexact PGD method, coined as Cadzow plug-and-play gradient descent (CPGD). The latter approximates the proximal steps by means of Cadzow denoising, a well-known denoising algorithm in FRI. We provide local fixed-point convergence guarantees for CPGD. Through extensive numerical simulations, we demonstrate the superiority of CPGD against the state-of-the-art in the case of non uniform time samples.Comment: 16 pages, 8 figure

Blind as a bat: audible echolocation on small robots

For safe and efficient operation, mobile robots need to perceive their environment, and in particular, perform tasks such as obstacle detection, localization, and mapping. Although robots are often equipped with microphones and speakers, the audio modality is rarely used for these tasks. Compared to the localization of sound sources, for which many practical solutions exist, algorithms for active echolocation are less developed and often rely on hardware requirements that are out of reach for small robots. We propose an end-to-end pipeline for sound-based localization and mapping that is targeted at, but not limited to, robots equipped with only simple buzzers and low-end microphones. The method is model-based, runs in real time, and requires no prior calibration or training. We successfully test the algorithm on the e-puck robot with its integrated audio hardware, and on the Crazyflie drone, for which we design a reproducible audio extension deck. We achieve centimeter-level wall localization on both platforms when the robots are static during the measurement process. Even in the more challenging setting of a flying drone, we can successfully localize walls, which we demonstrate in a proof-of-concept multi-wall localization and mapping demo.Comment: 8 pages, 10 figures, published in IEEE Robotics and Automation Letter

Spatial and temporal dynamics of ammonia oxidizers in the sediments of the Gulf of Finland, Baltic Sea

The diversity and dynamics of ammonia-oxidizing bacteria (AOB) and archaea (AOA) nitrifying communities in the sediments of the eutrophic Gulf of Finland (GoF) were investigated. Using clone libraries of ammonia monooxygenase (amoA) gene fragments and terminal restriction fragment length polymorphism (TRFLP), we found a low richness of both AOB and AOA. The AOB amoA phylogeny matched that of AOB 16S ribosomal genes from the same samples. AOA communities were characterized by strong spatial variation while AOB communities showed notable temporal patterns. At open sea sites, where transient anoxic conditions prevail, richness of both AOA and AOB was lowest and communities were dominated by organisms with gene signatures unique to the GoF. Given the importance of nitrification as a link between the fixation of nitrogen and its removal from aquatic environments, the low diversity of ammonia-oxidizing microbes across the GoF could be of relevance for ecosystem resilience in the face of rapid global environmental changes. (C) 2015 Elsevier Ltd. All rights reserved.Peer reviewe

Sparse Recovery of Strong Reflectors With an Application to Non-Destructive Evaluation

In this paper we show that it is sufficient to recover the locations of K strong reflectors within an insonified medium from three receive elements and 2K+1 samples per element. The proposed approach leverages advances in sampling signals with a finite rate of innovation along each element and rank properties from the Euclidean distance matrix construction across elements. With the proposed approach, it is not necessary to construct an image in order to identify strong reflective sources, which is why much fewer receive elements are needed. However, the assumed transmit scheme still uses a standard linear array in order to excite the entire medium with sufficient energy. The approach is validated with simulated data and a measurement that emulates a scenario in non-destructive evaluation

LiDAR-derived forest structure data and predictions of the locations of old-growth forests for Central Finland.

INTRO This archive contains data and analysis code for the Biodiversity Map -project conducted by Open Knowledge Finland (http://fi.okfn.org/projects/biodiversity-map/) LICENCE The files listed below are all released to the public domain under a CC0 public domain dedication (https://creativecommons.org/publicdomain/zero/1.0/) FILE DESCRIPTIONS FILE 1: background.zip Inside the archive is a comma-separated file "background.csv" containing LiDAR-derived forest structure variables for 2/3 of Central Finland. These were derived from 3 raster data sets describing forest canopy maximum height (mh), forest canopy cover (cc) and lidar return intensity (in). The rasters had resolutions of 6 metres, 6 metres and 2 metres, respectfully. An 18 m resolution grid was then used to aggregate the rasters into average, minimum and maximum values + standard deviations of the original variables. The original LiDAR data was made available by the National Land Survey of Finland. FILE 2: conservation.lambdas This file contains fitted parameters for the maxent model. For more information, check maxent documentation at https://www.cs.princeton.edu/~schapire/maxent/ FILE 3: conserved_swd.csv Forest structure variables at 18 meter resolution for old-growth conservation areas in Central Finland. A subset of background.csv. This file still has a header, the variables are the same as in background.csv FILE 4: grass_create_forest_rasters_from_las.sh A shell script used to convert LiDAR files to raster maps of forest structure with GRASS 7. FILE 5: lidar_coverage.png A map showing the extent of LiDAR data available for Central Finland when we did the analyses. FILE 6: maxent_model_run_product.sh A shell script used to fit the maximum entropy model to predict the locations of conservation-area-like forests in Central Finland. FILE 7: projection_product.csv The results of the maxent model in a comma separated file. The first row has the variable names: x,y,product_fit. x and y are coordinates in the CRS ETRS-TM35FIN (EPSG:3067). product_fit is "the probablility that this 18*18 meter grid cell is old-growth conservation area". FILE 8: README A file with a description of the dataset in human-readable form. VALIDATION FILES The data in these files was collected to validate the results of the aforementioned maxent model. The data were collected in a hierarchical sampling scheme: six randomly determinded unintersecting 9 km * 9 km landscape windows were chosen for sampling. From each window, three samples were taken. One sample from conservation areas, one sample from the "best" 10 % of forests as determined by the maxent model excluding conservation areas and one random sample. Not all windows contained conservation areas, and not all areas were accessible (islands, for example). In addition a few areas were skipped due to time constraints. The sampled points are identified by their lanscape window (suuralue), their sample (otos) and their sample number (mittauspiste). FILE 9: validation_felled.csv A comma separated list of those points that were not measured because they were felled. FILE 10: validation_gps_results_2016-09-07.csv A list of gps coordinates for all the sample points. product_fit is the value of the geographically closest prediction from the maxent model described above. FILE 11: validation_lying_deadwood_transects_2016-08-30.csv A comma separated file with data from deadwood transects. From each validation point, three 30 m long transects were made with 120 degree angles between them, and all lying deadwood more than 2 cm in diameter were measured. For some validation points, there were geographical obstructions which prevented the full 90 m of transect being surveyed, this is also recorded in the data. Each row holds measurements from one lying trunk. FILE 12: validation_relascope_2016-08-30.csv Relascope measurements from the validation points. Each row is measurements for one species from one validation point. Dead and alive trees are counted separately. MORE INFORMATION For more in-depth descritions of the files, read the file named README. For some auxilliary files and information, check our old hackathon repository on github: https://github.com/Koalha/bdm_hackatho

CPGD: Cadzow Plug-and-Play Gradient Descent for Generalised FRI

Finite rate of innovation (FRI) is a powerful reconstruction framework enabling the recovery of sparse Dirac streams from uniform low-pass filtered samples. An extension of this framework, called generalised FRI (genFRI), has been recently proposed for handling cases with arbitrary linear measurement models. In this context, signal reconstruction amounts to solving a joint constrained optimisation problem, yielding estimates of both the Fourier series coefficients of the Dirac stream and its so-called annihilating filter, involved in the regularisation term. This optimisation problem is however highly non convex and non linear in the data. Moreover, the proposed numerical solver is computationally intensive and without convergence guarantee. In this work, we propose an implicit formulation of the genFRI problem. To this end, we leverage a novel regularisation term which does not depend explicitly on the unknown annihilating filter yet enforces sufficient structure in the solution for stable recovery. The resulting optimisation problem is still non convex, but simpler since linear in the data and with less unknowns. We solve it by means of a provably convergent proximal gradient descent (PGD) method. Since the proximal step does not admit a simple closed-form expression, we propose an inexact PGD method, coined as Cadzow plug-and-play gradient descent (CPGD). The latter approximates the proximal steps by means of Cadzow denoising, a well-known denoising algorithm in FRI. We provide local fixed-point convergence guarantees for CPGD. Through extensive numerical simulations, we demonstrate the superiority of CPGD against the state-of-the-art in the case of non uniform time samples